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Complete the following using matrices. When you create a matrix,
label it. If a matrix does not clearly answer the question, please write a
sentence to explain your answer.
Shelly and Clint make dog houses. They call their company Canine Cabins.
Shelly builds the walls. Clint builds the roof and floor. Then Clint
attaches the roof and floor to the walls and Shelly paints it. Canine Cabins
come in two sizes. The walls of a small house require 25 square feet of wood
and 1 hour of labor. The roof and floor require 15 square feet of wood and
an hour of labor. The walls of a large house require 70 square feet of wood
and an hour of labor. The roof and floor of a large house use 30 square feet
of wood and an hour of labor.
- Compile this information into two 2 by 3 matrices (remember that have not used paint yet, but we will). You will have one matrix for walls and one for roof and floor.
- Using the matrices, determine how much wood, paint, and labor are used for each house before they are assembled if we build one large and one small house.
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A completed small houses requires 40 square feet of wood, 1 pint of
paint, and 3.5 hours of labor. A large house requires 100 square feet of
wood, 1.5 pints of paint, and 4 hours labor. Form the 2 by 3 matrix that represents the total units of each material required to complete each sizeof house.
- Determine how much wood, paint, and time are required to attach the roof and floor to the walls and paint the house for each size.
- If wood costs $0.50 per square foot, paint costs $6 per pint, and
Shelly and Clint earn $8 per hour, how much does each size house cost to
produce?
- This month, Canine Cabins had orders for 30 small houses and 20 large
houses. How much of each material do they need to fill the orders?
- How much money will they need to buy the material to fill the orders?
- If A is a 3 by 4 matrix, B is 2 by 4, and C is 2 by 3, list all the ways using (A or AT), (B or BT), and (C or CT) that you can multiply these three matrices together. Each matrix or its transpose must be used exactly once in each multiplication.
- Given
- Find the determinate of A.
- Solve the system Ax = b using Gaussian elimination or Gauss-Jordan elimination. Specify which you are using.
- Find the inverse of A.
- How would you prove that your solution to problem is actually the inverse of A?
- Create a matrix for which an inverse does not exist and explain why an inverse does not exist.
- Create a system for each of the following descriptions and explain why the system fits the description.
- Consistent and underdetermined.
- Consistent and uniquely determined.
- Inconsistent.
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